5=8q^2

Solution for 5=8q^2 equation:

5=8q^2

We move all terms to the left:

5-(8q^2)=0

a = -8; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-8)·5
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{10}}{2*-8}=\frac{0-4\sqrt{10}}{-16}
=-\frac{4\sqrt{10}}{-16}
=-\frac{\sqrt{10}}{-4}
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{10}}{2*-8}=\frac{0+4\sqrt{10}}{-16}
=\frac{4\sqrt{10}}{-16}
=\frac{\sqrt{10}}{-4}
$